1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Velocity based frictional force equations

  1. Sep 29, 2004 #1
    Im doing a problem with variable frictional forces.

    My main equation is -mkv^2=F . We are to assume the force driving the object remains constant, kinda like a boat on the lake full bore.

    So, I set my F=ma equation up.
    -mkv^2=m(dv/dt)

    Next I removed m and inverted both equations to solve for dt.
    -dv/(kv^2)=dt

    Next I intetegrated both sides seperately. I was taught to use a "dummy variable" by marking v and t somehow. I simply chose to use a superscript prime marking on my paper. anyhow... Ill use a little v for real velocity and big V for dummy velocity.
    (1/kV)|0 to v = t

    Isnt that (1/kv) - (1/0) ?

    This equation doesnt solve nicely. In my setup I am given the equation for velocity and only asked to show how I got it.
    V=Vo / (1 + Vo*kt)

    Please help... I posted part of this problem over in classical when I had a different problem with it, so please dont flame me for double posting or spamming the board. If thats your opinion I couldnt care less.

    TIA to anyone who helps!
     
  2. jcsd
  3. Sep 29, 2004 #2

    Pyrrhus

    User Avatar
    Homework Helper

    Let me see

    [tex] F = -mkv^2 [/tex]

    [tex] m \frac{dv}{dt} = -mkv^2 [/tex]

    [tex] -\frac{dv}{kv^2} = dt [/tex]

    [tex] \int^{v}_{v_{o}} -\frac{dv}{kv^2} = \int^{t}_{0} dt [/tex]

    [tex] \frac{1}{kv}]^{v}_{v_{o}} = t]^{t}_{0}[/tex]

    [tex] \frac{1}{kv} - \frac{1}{kv_{o}}= t - 0[/tex]
     
  4. Sep 29, 2004 #3
    Hey, cyclovenom!

    Thanks, all the examples we did in class used velocity starting at 0.. I didnt understand the part where we get limits of integration from. now it makes perfect sense, v=0 at t=0, so the lower limits are 0 and 0. in this case, v=Vo at t=0

    Thanks for helping me out! Im totally clear, AND im going to start using latex!! woot!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Velocity based frictional force equations
Loading...